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A321492 Numbers that can be written as (x + y)(x^2 + y^2), x > y > 0, in at least two ways. 2
12325, 98600, 117720, 146705, 206312, 263840, 332775, 378505, 400945, 500200, 651456, 687245, 734400, 741845, 773800, 788800, 799240, 941760, 1173640, 1327360, 1533195, 1540625, 1650496, 1735105, 1836680, 1943240, 2048320, 2050880, 2110720, 2217280, 2662200, 2704360, 2965685 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A321491 for numbers of the form (x+y)(x^2+y^2) = A321490(x,y) with x > y > 0.
LINKS
Geoffrey B. Campbell, (m+n)(m²+n²) in two different ways, LinkedIn Number Theory Group, Aug. 2018
EXAMPLE
12325 = (13+16)(13^2+16^2) = (3+22)(3^2+22^2).
98600 = (26+32)(26^2+32^2) = (6+44)(6^2+44^2).
117720 = (21+39)(21^2+39^2) = (8+46)(8^2+46^2).
146705 = (24+41)(24^2+41^2) = (14+47)(14^2+47^2).
206312 = (15+53)(15^2+53^2) = (32+42)(32^2+42^2).
263840 = (6+62)(6^2+62^2) = (33+47)(33^2+47^2).
PROG
(PARI) A321492_list(L=1e6)={my(S=[], T=List(), t); for(m=2, sqrtn(L, 3), while(#S&&S[1]<=m^3, S=S[^1]); for(n=1, m-1, if(L<t=(m+n)*(m^2+n^2), next(2), setsearch(S, t), listput(T, t); S=setminus(S, [t]), S=setunion(S, [t])))); Set(T)}
CROSSREFS
Sequence in context: A077186 A077189 A277947 * A237782 A248717 A184472
KEYWORD
nonn
AUTHOR
Geoffrey B. Campbell and M. F. Hasler, Nov 22 2018
STATUS
approved

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Last modified July 20 17:48 EDT 2024. Contains 374459 sequences. (Running on oeis4.)